树收缩与进化树
Tree Contractions and Evolutionary Trees
摘要：
进化树是一棵有根树，其中每个内部顶点至少有两个子节点，叶子上标有代表物种的不同符号。进化树对于模拟物种的进化历史非常有用。两棵进化树的一致子树是一棵进化树，它也是这两棵树的拓扑子树。本文给出了一个算法，以确定两棵各有n个叶子的树T_1和T_2的任何一致子树的最大可能叶子数。如果这些树的最大度d被一个常数限制，则时间复杂度为O（n log^2（n）），并且在最优的log（n）因子内。对于一般的d，这个算法的运行时间是O（n d^2 log（d）log^2（n）），或者O（n d sqrt（d）log^3（n））。
英文摘要：
An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of species. An agreement subtree of two evolutionary trees is an evolutionary tree which is also a topological subtree of the two given trees. We give an algorithm to determine the largest possible number of leaves in any agreement subtree of two trees T_1 and T_2 with n leaves each. If the maximum degree d of these trees is bounded by a constant, the time complexity is O(n log^2(n)) and is within a log(n) factor of optimal. For general d, this algorithm runs in O(n d^2 log(d) log^2(n)) time or alternatively in O(n d sqrt(d) log^3(n)) time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
